Actually, a least some cars (probably more than you think)/have some sort of "emergency" breaking signal, which often result in the usual breaking signal blinking for a while. You need to seriously slam the brakes to see it though. E.g: https://m.youtube.com/watch?v=j_osu1WgGMU
There is also a nice technology connection video talking about braking lights for electric cars and in general, which can be dangerous.
I don't know so much about EGS, but probably some of the following (most of which I don't use very often, I hope I recall correctly)